Simplify the following expression: $\dfrac{60p^2}{15p^5}$ You can assume $p \neq 0$.
$ \dfrac{60p^2}{15p^5} = \dfrac{60}{15} \cdot \dfrac{p^2}{p^5} $ To simplify $\frac{60}{15}$ , find the greatest common factor (GCD) of $60$ and $15$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $15 = 3 \cdot 5$ $ \mbox{GCD}(60, 15) = 3 \cdot 5 = 15 $ $ \dfrac{60}{15} \cdot \dfrac{p^2}{p^5} = \dfrac{15 \cdot 4}{15 \cdot 1} \cdot \dfrac{p^2}{p^5} $ $\phantom{ \dfrac{60}{15} \cdot \dfrac{2}{5}} = 4 \cdot \dfrac{p^2}{p^5} $ $ \dfrac{p^2}{p^5} = \dfrac{p \cdot p}{p \cdot p \cdot p \cdot p \cdot p} = \dfrac{1}{p^3} $ $ 4 \cdot \dfrac{1}{p^3} = \dfrac{4}{p^3} $